|"Is this all real? Or has this been happening inside my head?"
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The name "Katherine" comes from the Greek name Αικατερινη (Aikaterine). The etymology is debated: it could derive from the earlier Greek name ‘Εκατερινη (Hekaterine), which came from ‘εκατερος (hekateros) "each of the two"; it could derive from the name of the goddess HECATE; it could be related to Greek αικια (aikia) "torture"; or it could be from a Coptic name meaning "my consecration of your name".
- J. K. Rowling's Official Site (First mentioned)